Systems and methods to optimize partitioning of a data segment into data packets for channel encoding

ABSTRACT

Systems and methods to transmit data over multiple communication channels in parallel with forward error correction. An optimized number is determined to partition a data segment of a given size into the optimized number of original packets of the same size, by reducing the cost of transmitting dummy data added to the original packets due to the partition, the data fields added to communication packets to support decoding, and redundant packets that are expected to be transmitted via a plurality of parallel channels before the termination of the transmission, as well as the computation cost that increases as a function of the number of original packets. Copies of packets are generated by distributing the original packets to the copies as initial packets and generating each subsequent channel-encoded packet by rejecting useless channel-encoded packets in view of packets assumed to have been received prior to the transmission of the subsequent channel-encoded packet.

FIELD OF THE TECHNOLOGY

At least some embodiments disclosed herein relate to encoding data for reliable and efficient transmission over a communication system that does not have perfect fidelity, such as a communication system having parallel channels for communications made using forward error correction techniques.

BACKGROUND

Forward Error Correction (FEC) is a coding technique typically used for correcting errors in data transmission over communication channels. Using FEC a sender provides redundant data in the stream of communicated data to enable the recipient to detect errors in the received data and/or recover a copy of the original data from the correctly received data without requiring a reverse communication from the recipient to the sender to request retransmission of missing data or received data that has error.

FEC adds redundant data by transforming the original information into channel-encoded outputs using an algorithm. The original information may or may not appear literally in the encoded output. Outputs that include the unmodified input are systematic, while outputs that do not include the unmodified input are non-systematic. A recipient decodes the non-systematic outputs to reassemble the original information from the received outputs. Rateless erasure codes can potentially generate a limitless sequence of encoding symbols from a given set of original symbols such that the original symbols can be recovered from a subset of the encoding symbols of size equal to or larger than the number of original symbols. The rateless FEC does not have a fixed code rate.

U.S. Pat. No. 9,413,494, entitled “FEC-based Reliable Transport Control Protocols for Multipath Streaming”, discloses the transmission of forward-error corrected data, from a server device to a client device, via a plurality of parallel network paths. The client device reports, to the server device, the losses of the data in the network paths for the retransmission of the data lost in the network paths.

U.S. Pat. No. 7,249,291, entitled “System and Method for Reliably Communicating the Content of a Live Data Stream”, discloses a method to transmit a live data stream to a recipient using multiple channels, where a forward error correction algorithm is applied to generate FEC-encoded blocks.

U.S. Pat. No. 9,236,885, entitled “Systematic Encoding and Decoding of Chain Reaction Codes”, discloses that in certain applications it may be preferable to transmit the source symbols first, and then to continue transmission by sending output symbols. Such a coding system was referred to as a systematic coding system.

U.S. Pat. No. 9,015,564, entitled “Content Delivery System with Allocation of Source Data and Repair Data among HTTP Servers”, discloses a source server storing content in a source form, a broadcast sever generating and storing repair symbols, and repair servers requesting broadcast of repair data when byte-range requests from multiple receivers overlap.

U.S. Pat. App. Pub. No. 2010/0094955, entitled “Methods and Systems for using a Distributed Storage to its Maximum Bandwidth”, discloses a method to generate multiple coded fractional copies of a data segment, which are stored in multiple storage devices. A subset of the coded copies will be fully downloaded for data recovery, and in case of recovery failure, more coded copies will be fully downloaded.

U.S. Pat. No. 8,078,746, entitled “Distribution Method, Preferably Applied in a Streaming System”, discloses a method to generate, at peer receivers of a network, FEC-coded feed packets of the portion of the broadcast data they have received, so that all peer receivers can download sufficient feed packets from any other peer receivers to recover the entire broadcast data.

U.S. Pat. No. 8,996,946, entitled “Application of Fountain Forward Error Correction Codes in Multi-link Multi-path Mobile Networks”, discloses a method to generate different on-the-fly FEC encoded packets of a data segment and send these packets through different unreliable paths that are coupled with a receiver until the receiver has acknowledged or the time is out.

U.S. Pat. App. Pub. No. 2014/0269289, entitled “Method and Apparatus for Improving Communication Performance through Network Coding”, discloses a method to generate different on-the-fly network coding encoded packets of a data segment and send these packets through different unreliable paths that are coupled with a receiver. The receiver may send intermediate feedback to the transmitter to manage retransmissions. In case the data segment cannot be fully recovered, partial recovery will be attempted.

U.S. Pat. No. 9,455,750, entitled “Source Block Size Selection”, discloses techniques to select a source block size to reduce reception overhead in a communication system that partitions a media stream into source blocks of the selected size, divides each of the source block into source symbols that are encoded to generate repair symbols for transmission over a network.

The entire disclosures of the above identified patents are hereby incorporated herein by reference.

BRIEF DESCRIPTION OF THE DRAWINGS

The embodiments are illustrated by way of example and not limitation in the figures of the accompanying drawings in which like references indicate similar elements.

FIG. 1 shows a technique to transmit a data segment via FEC over multiple parallel channels according to one embodiment.

FIG. 2 shows a technique to transmit a data segment via FEC over multiple parallel channels using an initial systematic phase according to one embodiment.

FIG. 3 shows a technique to transmit a data segment via FEC over multiple parallel channels using encoded packets that are linearly independent of their base sets according to one embodiment.

FIG. 4 shows scheduling of systematic packets over multiple parallel channels according to one embodiment.

FIG. 5 shows the identification of the composition of a channel-encoded packet according to one embodiment.

FIG. 6 shows a system to transmit data packets using multiple channels according to one embodiment.

FIG. 7 shows a method to generate a channel-encoded packet according to one embodiment.

FIG. 8 shows a method to transmit a data segment according to one embodiment.

FIG. 9 illustrates an overhead cost in data communication for transmitting a data segment by dividing the data segment into a plurality of data packets for forward error control.

FIG. 10 illustrates the data structure of a communication packet of one embodiment.

FIG. 11 illustrates various cost considerations in the transmission of a data segment using a forward error correction technique.

FIG. 12 shows a method to transmit a data segment according to one embodiment.

FIG. 13 shows a data processing system on which the methods of the present disclosure can be implemented.

DETAILED DESCRIPTION

The following description and drawings are illustrative and are not to be construed as limiting. Numerous specific details are described to provide a thorough understanding. However, in certain instances, well known or conventional details are not described in order to avoid obscuring the description. References to one or an embodiment in the present disclosure are not necessarily references to the same embodiment; and, such references mean at least one.

At least some embodiments disclosed herein provide solutions to improve the efficiency, reliability, and overall speed of data transmission via multiple communication channels, in a system as illustrated in FIG. 1. The data transmission technique uses a rateless FEC technique, which partitions the original data segment into original packets of an equal-length and generates channel-coded packets from linear combinations of various subsets of the original packets.

FIG. 1 shows a technique to transmit a data segment via FEC over multiple parallel channels according to one embodiment.

In FIG. 1, a data segment (111) is transmitted via a plurality of parallel communication channels (105, 107, . . . , 109). The use of the parallel communication channels (105, 107, . . . , 109) generally increases the overall speed of the transmission of the data segment (111).

However, the actual performances of the individual communication channels (105, 107, . . . , 109) may vary at the time of transmission. Packets transmitted in one or more of the channels (e.g., 105, 107, . . . , or 109) may have longer, random delays than other packets transmitted via others channels (e.g., 105, 107, . . . , or 109). As a result, the sequence of the combined set of packets received in a recipient device from the channels (105, 107, . . . , 109) is randomized at the time of transmission.

Thus, it is a challenge to schedule the packets for the transmission in the communication channels (105, 107, . . . , 109) with reduced redundancy data and a reduced time period during which a sufficient number of useful packets are received via the parallel communication channels (105, 107, . . . , 109) for the reconstruction of the recovered data segment (113) that is the same as the original data segment (111).

In FIG. 1, the data segment (111) is partitioned (101), or divided, into a plurality of packets (121, 123, 125, . . . , 127) of the same length. Dummy bytes may be padded so that the packets (121, 123, 125, . . . , 127) have the same length and thus allow the use of a forward error correction technique. Using a forward error correction technique, the system channel encodes (103) the original packets (121, 123, 125, . . . , 127) to generate different channel-encoded copies (115. 117, . . . , 119) of the data segment (111) that carry redundant information in the copies (115, 117, . . . , 119) for the respective channels (105, 107, . . . , 119).

For example, in FIG. 1, a typical channel-encoded packet (e.g., 131, 133, 135, . . . , 139; 141, 143, 145, . . . , 149; . . . ; 151, 153, 157, . . . , or 159) generated using a typical forward error correction technique is a predetermined function of a random subset of original packets (121, 123, 125, . . . , 127). The predetermined function typically generates a linear combination of the subset of the original packets (121, 123, 125, . . . , 127) (e.g., through an exclusive or (XOR) operation) as a channel-encoded packet. When a sufficient number of channel-encoded packets are received via the channels (105, 107, . . . , 109), the received set of channel-encoded packets can be decoded via the respective forward error correction technique to provide the original set of packets (121, 123, 125, . . . , 127) and thus the recovered data segments (113).

In FIG. 1, the individual channels (e.g., 105, 107, . . . , or 109) may be reliable in the quality of data transmission (e.g., using a reliable protocol). When there is a missing packet or a packet having an error is received, the retransmission of the missing packet or packet having an error can be requested through any channels (e.g., 105, 107, . . . , or 109) using an appropriate protocol. However, the speed performances of channels (e.g., 105, 107, . . . , or 109) may be not be consistent, which incurs delays and duplications to the retransmissions. Embodiments disclosed herein provide solutions to improve the performance of the system by reducing duplicated (and thus useless) data and reducing the time period for the transmission of a sufficient set of useful packets for the recovery of the data segment (113).

In some instances, it is desirable to use separate transmitters to send the copies (115, 117, . . . , 119) through the channels (105, 107, . . . , 109) independently from each other. The transmitters may not have communications with each other to coordinate their transmissions of the copies (115, 117, . . . , 119). The system of FIG. 1 is configured such that when a recipient device receives a combined set of sufficient packets from channels (105, 107, . . . , 109), the recipient device can generate, from the combined set of received packets, the recovered data segment (113) that is the same as the original data segment (111), without having to wait for the completion transmission of the copies (115, 117, . . . , 119). The recipient device may simply terminate its receiving operations before the complete transmission of the copies (115, 117, . . . , 119) and/or request the termination of the transmission operations.

For example, when a combined set of sufficient packets is received for the recovered data segment (113), the recipient device provides an indication to the transmitting system to terminate the transmission of the remaining packets of the copies (115, 117, . . . , 119) in the channels (105, 107, . . . , 109), such that the network resources can be used for other transmission tasks.

For example, the recipient device may use the channels (115, 117, . . . , 119) to request the respective transmitters coupled to the channels (115, 117, . . . , 119) to terminate their transmission of their copies (e.g., 115, 117, . . . , 119). Alternatively, the recipient device may notify a centralized server, using one of the channels (105, 107, . . . , 109) or a separate communication channel, which server then further notifies the respective transmitters coupled to the respective channels (115, 117, . . . , 119) to terminate their transmissions.

The system of FIG. 1 can be further improved by distributing the original packets as initial packets (or leading packets) in the copies (115, 117, . . . , 119) that are transmitted prior to the transmission of channel-encoded packets (or non-systematic) of the respective copies (115, 117, . . . , 119), as illustrated in FIG. 2.

Alternatively or in combination, the system of FIG. 1 can be further improved by rejecting, in the random selection of the original packets for channel-encoding using the forward error correction technique, channel-encoded packets that do not, or are not likely to, contribute to the recovered data segment (113), in view of a base set of packets that have been, or likely, received by the recipient device before the transmission of such packets. Thus, data redundancy is reduced without impacting the performance of forward error correction, as illustrated in FIG. 3.

In general, the techniques of FIG. 2 and FIG. 3 can be combined.

Further, for a given number of the original packets (121, 123, 125, . . . , 127) and a given number of the channels (e.g., 105, 107, . . . , 109), the system can predetermine the composition of the channel-encoded packets (131, 133, 135, . . . , 139; 141, 143, 145, . . . , 149; . . . ; 151, 153, 157, . . . , 159). The composition of a channel-encoded packet (131, 133, 135, . . . , 139; 141, 143, 145, . . . , 149; . . . ; 151, 153, 157, . . . , or 159) identifies the identity/identities of the subset of the original packets (121, 123, 125, . . . , 127) used to generate the channel-encoded packet. For example, each of the original packets (121, 123, 125, . . . , 127) can be identified based on its sequence/position number in the sequence of the original packets (121, 123, 125, . . . , 127) (or another type of identification symbol) without its actual data of the original packet. The compositions of the channel-encoded packets (131, 133, 135, . . . , 139; 141, 143, 145, . . . , 149; . . . ; 151, 153, 157, . . . , 159) for the encoded copies (115, 117, . . . , 119) can be stored without the actual data of the original packets. When the actual data of the original packets (121, 123, 125, . . . , 127) is available, the compositions of the channel-encoded packets (131, 133, 135, . . . , 139; 141, 143, 145, . . . , 149; . . . ; 151, 153, 157, . . . , 159) are retrieved to combine the respective original packets (121, 123, 125, . . . , 127) identified by the compositions to generate the respective channel-encoded packets (131, 133, 135, . . . , 139; 141, 143, 145, . . . , 149; . . . ; 151, 153, 157, . . . , 159).

For example, at the time of the transmission, a transmitter receives the set of original packets (121, 123, 125, . . . , 127) and the sequence of compositions for the scheduled sequence of channel-encoded packets (e.g., 131, 133, 135, . . . , 139; 141, 143, 145, . . . , 149; . . . ; or 151, 153, 157, . . . , 159). The transmitter combines the original packets (121, 123, 125, . . . , 127) according to the compositions to generate the respective channel-encoded packets just before transmitting the generated packets for transmission over the respective channel (e.g., 105, 107, . . . , or 109). Thus, when the recipient device signals for the early termination of the transmission, the remaining channel-encoded packets do not have to be actually generated and/or stored.

FIG. 2 shows a technique to transmit a data segment via FEC over multiple parallel channels using an initial systematic phase according to one embodiment. For example, the technique of FIG. 2 can be used in a system illustrated in FIG. 1.

In FIG. 2, each copy (e.g., 115, 117, . . . , or 119) scheduled to be transmitted via a respective channel (e.g., 105, 107, . . . , 109) has a sequence of scheduled packets (121, 127, 135, . . . , 139; 123, 143, 145, . . . , 149; . . . ; or 125, 153, 157, . . . , 159). The copies (115, 117, . . . , 119) have a set of initial packets (121, 123, . . . , 125, 127) that correspond to the set of original packets (121, 123, 125, . . . , 127).

In each of the channels (105, 107, . . . , 109), the initial packets of a respective copy (e.g., 115, 117, . . . , 119) are transmitted before other packets of the respective copy (e.g., 115, 117, . . . , 119). For example, the initial packets (121, 127) of Copy X (115) are transmitted before the transmission of packets (135, . . . , 139) of Copy X (115); the initial packet (123) of Copy Y (117) is transmitted before the transmission of packets (143, 145, . . . , 149) of Copy Y (117); and the initial packet (125) of Copy Z (119) is transmitted before the transmission of packets (153, 155, . . . , 159) of Copy Z (119).

The initial packets (121, 123, . . . , 125, 127) are generated/identified by distributing the set of original packets (121, 123, 125, . . . , 127) to the copies (115, 117, . . . , 119).

For example, when the channels (105, 107, . . . , 109) have the same nominal/average/expected transmission speed, the original packets (121, 123, 125, . . . , 127) can be distributed to the copies (115, 117, . . . , 119) substantially evenly. For example, the original packets (121, 123, 125, . . . , 127) can be distributed one at a time to the copies according to a round-robin scheme until all of the original packets (121, 123, 125, . . . , 127) are distributed to the copies (115, 117, . . . , 119). Alternatively, the system computes the average number of original packets (e.g., by dividing the number of packets by the number of channels and taking the integer part of the result), assigns the average number of original packets to each copy, and randomly distribute the remaining, unassigned packets one at a time to the copies (115, 117, . . . , 119) until all of the original packets (121, 123, 125, . . . , 127) are assigned.

In instances where the channels (105, 107, . . . , 109) have substantially different nominal/average/expected transmission speeds, the original packets (121, 123, 125, . . . , 127) can be distributed to the copies (115, 117, . . . , 119) in a ratio approximately equal to the ratio of their nominal/average/expected transmission speeds.

Once all original packets have been distributed as the initial packets of the copies (e.g., 115, 117, . . . , 119), channel-encoded packets (e.g., 135, 143, 145, . . . , 149, 153, 157, . . . , 159) are generated and added to the copies (e.g., 115, 117, . . . , 119). Each channel-encoded packet (e.g., 135) of a given copy (e.g., 115) can be generated from a linear combination of a random selected subset of all the original packets (e.g., 121, 123, 125, . . . , 127).

Preferably, each channel-encoded packet (e.g., 135) of a given copy (e.g., 115) can be generated from a linear combination of a random selected subset of the original packets (e.g., 123, 125) carried by other copies (e.g., 117, . . . , 119) another than the given copy (e.g., 115). In other words, the set of original packets (e.g., 121, 127) carried by the given copy (e.g., 115) is not used for the generation of the channel-encoded packets (e.g., 135, . . . , 139) of this given copy (e.g., 115). This is because by the time a channel-encoded packet (e.g., 135) of this given copy (e.g., 115) is received, the recipient device will already have received all the original packets (e.g., 121, 127) carried by this given copy (e.g., 115). Excluding these original packets will reduce both computational complexity and the probability of generating useless channel-encoded packets.

FIG. 3 shows a technique to transmit a data segment via FEC over multiple parallel channels using channel-encoded packets that are linearly independent of their base sets according to one embodiment. For example, the technique of FIG. 3 can be used in a system illustrated in FIGS. 1 and/or 2.

In FIG. 3, the transmission of data packets within each channel (105, 107, . . . , 109) is reliable. Thus, at the time of the transmission of a subsequent packet (e.g., 135) in the channel (e.g., 105), the recipient device has correctly received the data packets (e.g., 131, 133) that have been transmitted in the same channel (e.g., 105) before the subsequent packet (e.g., 135). Thus, a candidate for the subsequent channel-encoded packet (e.g., 135) that is linearly dependent of the received data packets (e.g., 131, 133) is useless and can be rejected.

Further, by the time of the transmission of the subsequent packet (e.g., 135) in the channel (e.g., 105), it is very likely that the recipient device has received the initial packets (e.g., 141, . . . , 151) transmitted in other channels (e.g., 107, . . . , 109). The subsequent packet (e.g., 135) can be considered to have a base set (161) of packets (131, 133, 141, . . . , 151) that include all the packets (e.g., 131, 133) in the same channel (e.g., 105) that are scheduled to be transmitted before the subsequent packet (e.g., 135) and the initial packets (e.g., 141, . . . , 151) of the other channels (e.g., 107, . . . , 109) that are very likely to have reached the recipient device via other channels (e.g., 107, . . . , 109) before the transmission of the subsequent packet (e.g., 135). A candidate for the subsequent packet (e.g., 135) that is linearly dependent of the base set is most likely useless and thus can be rejected.

To ensure/improve the usefulness of the channel-encoded packet (135), the system of FIG. 3 is configured to identify the subsequent channel-encoded packet (135) such that it is linearly independent of the base set (161) of packets (131, 133, 141, . . . , 151), where the base set (161) includes all the packets (e.g., 131, 133) that are scheduled in the copy (115) before the subsequent channel-encoded packet (135), and the certain initial packets (e.g., 141, . . . , 151) of the other copies (117, . . . , 119).

In determining the initial packets (e.g., 141, . . . , 151) of the other copies (117, . . . , 119) for the base set (161) for the subsequent packet (135), it is assumed that the base set (161) is insufficient to generate the recovered data segment (113), which triggers the need to transmit the subsequent packet (135) in the channel (105). Thus, the base set (161) is identified to include less packets than the entire set of the original packets (121, 123, 125, . . . , 127).

Further, the other channels (e.g., 107, . . . , 109) are assumed to have transmitted their initial packets according to their ratio of the nominal/average/expected transmission speeds. For example, when the other channels (e.g., 107, . . . , 109) have an equal nominal/average/expected transmission speed, the same number of initial packets are selected from the other copies (e.g., 117, . . . , 119) for the base set (161) of the subsequent packet (135).

For example, the initial packets (e.g., 141, . . . , 151) of the other copies (117, . . . , 119) can be selected for the base set (161) of the subsequent packet (135) of the copy (115) in the follow manner. The system determines a remaining number of packets to be transmitted in the other copies (117, . . . , 119) by reducing the number of original packets (121, 123, 125, . . . , 127) by the number of initial packets in the copy (115) up to and including the subsequent packet (135). The system then distributes the remaining number of packets to the other copies (117, . . . , 119) (e.g., according to their ratio of nominal/average/expected transmission speeds). The numbers of packets distributed to the other copies (117, . . . , 119) identifies the corresponding numbers of initial packets (e.g., 141, . . . , 151) of the other copies (117, . . . , 119) that are included in the base set (161) for the subsequent packet (135) of the copy (115).

For example, there are K original packets (121, 123, 125, . . . , 127); the subsequent packet (135) is the k'th packet in the copy (115); and the system uses M channels (105, 107, . . . , 109) to transmit the M copies (115, 117, . . . , 119) respectively in parallel. The remaining number of packets to be distributed to the other copies (117, . . . , 119) is (K−k). When the other channels (107, . . . , 109) have the same nominal/average/expected transmission speed, the other copies (e.g., 117, . . . , 119) have an average of (K−k)/(M−1) initial packets of their respective copies (117, . . . , 119) that are selected as the base set (161) for the subsequent packet (135). When (K−k)/(M−1) is not an integer, and d is the integer that is closest to (K−k)/(M−1) but no larger than (K−k)/(M−1), the base set (161) may be selected to include the initial d packets of each of the other copies (e.g., 117, . . . , 119). Optionally, the base set (161) may further include an additional initial packet from (K−k)−d*(M−1) randomly selected copies of the other copies (e.g., 117, . . . , 119).

Further, when the channels (105, 107, . . . , 109) have the same nominal/average/expected transmission speed, the number of initial packets selected from each other copies (e.g., 117, . . . , 119) is not more than k−1, since at the time of the transmission of the k'th packet in channel (105), no more than k−1 packets of each other copies (e.g., 117, . . . , 119) are expected to have been transmitted through each other channels (107, . . . , 109).

The compositions of the channel-encoded packets can be used to identify whether or not a candidate for the subsequent packet (135) is linearly dependent of the base set (161). The composition of a channel-encoded packet (e.g., 135) identifies a subset of the original packets (121, 123, 125, . . . , 127) that are used in the generation of the channel-encoded packet (e.g., 135). More specifically, the composition of the channel-encoded packet (e.g., 135) identifies which of the original packets (121, 123, 125, . . . , 127) are used in the generation of the channel-encoded packet (e.g., 135) and which are not. For example, the composition of a channel-encoded packet can be represented by a vector of symbols, where the i'th symbol of vector is either zero when the i'th original packet is not used in the generation of the channel-encoded packet, or one when the i'th original packet is used in the generation of the channel-encoded packet.

The subsequent packet (135) can be selected such that the composition vector of the subsequent packet (135) is linearly independent of the composition vectors of the packets (131, 133, 141, . . . , 151) in the base set (161). For example, when a forward error correction technique is used to select a random subset of the original packets (121, 123, 125, . . . , 127) for the generation of the subsequent packet (135), the system checks whether the random subset has a composition that is linearly independent of the compositions of the packets in the base set (161); if so, the random subset is accepted as the composition of the subsequent packet (135); otherwise, the random subset is rejected, and another random subset is selected.

Since each subsequent packet (e.g., 135) scheduled in a copy (e.g., 115) is at least linearly independent of the packets scheduled before the subsequent packet in the same copy (e.g., 115), the copy (e.g., 115) requires at most the same count of packets (e.g., 131, 133, 135, . . . , 139) as the original packets (121, 123, 125, . . . , 127).

FIG. 4 shows scheduling of systematic packets over multiple parallel channels according to one embodiment. For example, the scheduling technique of FIG. 4 can be used in the system of FIG. 2.

In FIG. 4, the initial packets (121, 123, . . . , 125, 127) of the copies (115, 117, . . . , 119) are generated by round-robin allocation (163) of the original set of packets (121, 123, . . . , 125, 127) to the copies (115, 117, . . . , 119). As discussed above, the round-robin allocation (163) can be performed according to the ratio of the nominal/average/expected transmission speeds of channels used to transmit the copies (115, 117, . . . , 119) in parallel.

The round-robin allocation (163) can be performed without the actual data of the original packets (121, 123, . . . , 125, 127). The compositions of the initial systematic packets (121, 123, . . . , 125, 127) identify the respective original packets (121, 123, . . . , 125, 127) that are literally copied into the respective initial systematic packets (121, 123, . . . , 125, 127).

Subsequent channel-encoded packets for the copies (115, 117, . . . , 119) can be generated using any forward error correction technique in general and more preferably, in a way as illustrated in FIG. 3 or FIG. 5.

FIG. 5 shows the identification of the composition (166) of a channel-encoded packet (143) according to one embodiment. For example, the scheduling technique of FIG. 5 can be used in combination the techniques of FIG. 3 or FIG. 4. Although FIG. 5 illustrates an example where a set of the initial packets of the copies (115, 117, . . . , 119) are original packets, the method of FIG. 5 can also be applied to the use of channel-encoded initial packets in the copies (115, 117, . . . , 119).

In FIG. 5, a base set (165) is identified for the packet (143) scheduled to be transmitted after the packet (123) in the copy (117). The base set (165) is insufficient to reconstruct the entire set of the original packets (121, 123, . . . , 125, 127); and the base set (165) includes packets that are expected (or most likely) to have been received in a recipient device at the time the packet (143) is to be transmitted if the copies (115, 117, . . . , 119) are transmitted in parallel using multiple channels (e.g., 105, 107, . . . , 109). Examples of methods to identify the base set (165) are discussed above in connection with FIG. 3.

In FIG. 5, the compositions of the packets in the base set (165) are used to identify the composition (166) of the channel-encoded packet (143). Specifically, the composition (166) is generated by randomly selecting (167) a subset from the original packets (121, 123, . . . , 125, 127) (e.g., according to a distribution function of a forward error correction technique). In FIG. 5, solid boxed packets (e.g., 121, . . . , 125) in the composition (166) are illustrated as the packets of the subset that is selected for the generation of the channel-encoded packet (143); and the dash boxed packets (e.g., 123, . . . , 127) in the composition (166) are illustrated as the packets not selected for the generation of the channel-encoded packet (143). In FIG. 5, the random selection of the subset is repeated (e.g., according to the predetermined distribution function) until the composition vector of the selected subset is linearly independent of the composition vectors of the packets (e.g., 121, 123, . . . , 125) in the base set (165). The selected composition (166) of the channel-encoded packet (143) ensures that the packet (143) is useful, and thus not redundant, when it is used in combination with the packets (121, 123, . . . , 125) in base set (165) during channel decoding. Since at least some useless packets are pre-filtered during the selection of the compositions of the subsequent channel-encoded packets, the technique improved the efficiency in the use of the network channels during the transmission of the channel-encoded copies (115, 117, . . . , 119).

Further, to reduce computational complexity the composition (166) can be selected such that the packets (e.g., 121, . . . , 125) selected in the composition (166) to compute the channel-encoded packet (143) of the copy (117) do not include the original packets (e.g., 123) that are scheduled to be transmitted in the copy (117) before the channel-encoded packet (143) and/or do not include the original packets (121, 123, . . . , 125) in the base set (165). For example, the random selection of packets for the composition (166) may be limit to the subset of original packets that do not include the leading original packets (e.g., 123) of the copy (117) and/or the original packets (121, 123, . . . , 125) in the base set (165) to reduce both computational complexity in channel-encoding and the probability of generating a composition that is linearly dependent of the base set (165).

The composition (166) can be stored as an intermediate result such that at a later time when the actual packet (143) is to be used (e.g., for transmission over a communication channel), the composition (166) can be used to select original packets that are combined (169) (e.g., via exclusive or (XOR) or another linear combination function) to generate the content of the channel-encoded packet (143).

Since the scheduling of the subsequent packet (143) does not require the actual data/content of the original packets (121, 123, . . . , 125, 127), the selection (167) of original packets (121, 123, . . . , 125, 127) for further subsequent packets can be performed in a similar way based on the stored compositions of the packets that have already scheduled in the copies (115, 117, . . . , 119). Thus, the compositions of all of the packets in the copies (115, 117, . . . , 119) can be pre-computed and stored for the predetermined number of original packets (121, 123, . . . , 125, 127) without the actual packet data/content. This allows the scheduling of the packets before transmission and before the content of the packets (121, 123, . . . , 125, 127) becomes available. At the time of transmission, a transmitter retrieves the compositions of the packets scheduled in the respective copy (e.g., 117) and combines the original packets according to the compositions (e.g., 166) to generate the packet (e.g., 143) just in time for its transmission.

FIG. 6 shows a system to transmit data packets using multiple channels according to one embodiment. For example, the system of FIG. 6 can be implemented to use techniques of FIGS. 1, 2 and/or 3.

In FIG. 6, a scheduler (225) computes the sequences (235, 237, . . . , 239) of compositions of channel-encoded packets (e.g., 255, 257, . . . , 259) based on the number (221) of the original packets (121, 123, 125, . . . , 127) from which the channel-encoded packets (e.g., 255, 257, . . . , 259) are generated and the number (223) of the channels (105, 107, . . . , 109) that will be used for the transmissions of the channel-encoded packets (e.g., 255, 257, . . . , 259).

For example, the compositions of initial channel-encoded packets of the sequences (235, 237, . . . , 239) can be determined using a method of FIG. 4; and compositions of subsequent channel-encoded packets of the sequences (235, 237, . . . , 239) can be determined using a method of FIG. 5.

Alternatively, the compositions of at least some of the initial channel-encoded packets of the sequences (235, 237, . . . , 239) and/or the subsequent channel-encoded packets of the sequences (235, 237, . . . , 239) can be determined based on a random process without using the methods of FIG. 4 and/or FIG. 5.

In FIG. 6, the sequences (235, 237, . . . , 239) of compositions are provided to the transmitters (245, 247, . . . , 249) that are coupled with the respective channels (105, 107, . . . , 109) for the transmission of the respective channel-encoded packets (255, 257, . . . , 259). The transmitters (245, 247, . . . , 249) receive the same copy of the original packets (121, 123, 125, . . . , 127). Using the respective sequences (235, 237, . . . , 239) of compositions, the transmitters (245, 247, . . . , 249) apply a predetermined function (e.g., XOR) to original packets identified in the respective compositions to generate the sequences of channel-encoded packets (255, 257, . . . , 259) for transmission to the recipient device (229).

Preferably, each of the transmitters (245, 247, . . . , 249) generates a subsequent channel-encoded packet for a sequence (e.g., 235, 237, . . . , or 239) after the channel-encoded packets scheduled before the subsequent channel-encoded packet in the sequence have been successfully transmitted through the respective channel (e.g., 105, 107, . . . , 109).

Alternatively, channel-encoded packets (e.g., 255, 257, . . . , 259) may be pre-generated before the transmission. For example, the scheduler (225) may generate the sequences of the channel-encoded packets (e.g., 255, 257, . . . , 259) and provide the channel-encoded packets (e.g., 255, 257, . . . , 259) directly to the transmitters (e.g., 245, 247, . . . , 249), instead of providing the combination of the original packets (121, 123, 125, . . . , 127) and the sequences (235, 237, . . . , 239) of compositions of the channel-encoded packets (255, 257, . . . , 259). In some instances, some of the transmitters (e.g., 247) are configured to receive the sequence channel-encoded packets (e.g., 257), while other transmitters (e.g., 245) are configured to receive the sequences (e.g., 235) of compositions and the original packets (e.g., 121, 123, 125, . . . , 127) to generate the channel-encoded packets (e.g., 255) on-the-fly during their transmission.

In FIG. 6, the transmitters (245, 247, . . . , 249) use the channels (105, 107, . . . , 109) to transmit the channel-encoded packets (255, 257, . . . , 259) in parallel. However, due to the real-time performance variations, the sequence of the received packets (227) obtained by the recipient device (229) from the channels (105, 107, . . . , 109) may be partially randomized. When the recipient device (229) receives a sufficient number of channel-encoded packets via any combination of the channels (105, 107, . . . , 109), the recipient device (229) can fully recover the sequence of original packets (121, 123, 125, . . . , 127) using the forward error correction technique for channel decoding.

The system of FIG. 6 allows the transmitters (245, 247, . . . , 249) to transmit their respective sequences of encoded packets (255, 257, . . . , 259) without coordination with each other. The sequences (e.g., 235, 237, . . . , 239) of the encoded packets (e.g., 255, 257, . . . , 259) are predetermined and are not changed during the transmission. Thus, there is no need for reverse communications from the recipient device (229) to the transmitters (245, 247, . . . , 249) and/or the scheduler (225) for the coordination of the generation of the channel-encoded packets across the channels (105, 107, . . . , 109).

Optionally, the recipient device (229) individually requests at least some of the transmitters (245, 247, . . . , 249) to terminate their transmissions, after the set of received packets (227) is sufficient to recover the original sequence of the original packets (121, 123, 125, . . . , 127) and before the respective transmitters (245, 247, . . . , 249) complete the transmission of their complete sequences (235, 237, . . . , 239) of encoded packets.

The recipient device may deliver any received original packets to an application (e.g., a video player) in order, determine whether any of the received channel-encoded packet is useful, and if enough useful packets have been received, it causes the termination of the transmission across the parallel channels (105, 107, . . . , 109), and applies FEC decoding to recover all of the original packets (121, 123, 125, . . . , 127).

FIG. 7 shows a method to generate a channel-encoded packet according to one embodiment. For example, the method of FIG. 7 can be used by the scheduler (225) of FIG. 6 in the determination/selection (167) of the composition (166) of a packet (143) illustrated in FIG. 5, or the generation of the subsequent packet (135) illustrated in FIG. 3.

In FIG. 7, the scheduler (225) is configured to: determine (171) a first number of packets (e.g., 131, 133) scheduled to be transmitted in a first channel (e.g., 105) before a channel-encoded packet (135); and determine (173) a second number of packets (e.g., 141, . . . , 151) scheduled to be transmitted in second channels (e.g., 107, . . . , 109). The first number of packets (e.g., 131, 133) and the second number of packets (e.g., 141, . . . , 151) form a base set (161), where the packets (e.g., 131, 133, 141, . . . , 151) in the base set (161) are less than the total number of original packets (e.g., 121, 123, 125, . . . , 127) to be transmitted via the first and second channels (e.g., 105, 107, . . . , 109).

The scheduler (225) identifies (175) a randomly selected subset of the original packets (121, 123, . . . , 127) for the generation of the encoded packet (e.g., 135) according to a forward error correction coding method. If it is determined (177) that the subset is linearly dependent of the base set (161) (e.g., based on their composition vectors), the subset is rejected; and the computing device identifies (175) another randomly selected subset, until it is determined (177) that the subset is linearly independent of the packets (e.g., 131, 133, 141, . . . , 151) in the base set (161). The identification of the subset provides the composition of the encoded packet (e.g., 135) scheduled to be transmitted after the first number of packets (e.g., 131, 133) in the first channel (e.g., 105).

In FIG. 7, the scheduler (225) (or the transmitters (245, 247, . . . , 249), or another device) generates (179) the encoded packet (135) from a linear combination (e.g., XOR) of the subset for transmission in the first channel (105) after the first number of packets (e.g., 131, 133).

FIG. 8 shows a method to transmit a data segment according to one embodiment. For example, the method of FIG. 8 can be implemented in a system illustrated in FIG. 6.

In FIG. 8, a scheduler (225) is configured to schedule (181) the transmission of a sequence of original packets (121, 123, . . . , 125, 127) in the plurality of channels (105, 107, . . . , 109) by distributing the original packets (121, 123, . . . , 125, 127) to the channels using a round-robin method (163). Preferably, the original packets (121, 123, . . . , 125, 127) distributed to the plurality of channels (105, 107, . . . , 109) function as the systematic channel-encoded packets scheduled to be transmitted in the respective channels before the transmission of other subsequent non-systematic channel-encoded packets.

In FIG. 8, for each subsequent packet (e.g., 135) to be transmitted in each respective channel (e.g., 105) of the channels, the scheduler (225) identifies a base set (e.g., 161) of packets (e.g., 131, 133, 141, . . . , 151), which may include all packets (e.g., 131, 133) that are scheduled for transmission in the respective channel (e.g., 105) before the subsequent packet (e.g., 135) and optionally one or more packets (e.g., 141, . . . , 151) scheduled for parallel transmission in each of the channels (e.g., 107, . . . , 109) other than the respective channel (e.g., 105) for the subsequent packet (e.g., 135).

In FIG. 8, the scheduler (225) identifies (185), for the subsequent packet (e.g., 135), a subset of the original packets (e.g., 123, . . . , 125, 127 as identified by the composition (166) of a subsequent packet (e.g., 143) in FIG. 5), such that the composition vector of the subset is linearly independent of the composition vectors of the packets in the base set. The subset can be randomly selected according to a forward error correction technique until the subset has a composition that is linearly independent of the compositions of the packets in the base set.

In FIG. 8, the scheduler (225) stores (187), for the subsequent packet (e.g., 135), the identifications of the subset of the original packets as the composition of the subsequent packet (e.g., 135).

After the original packets (121, 123, 125, . . . , 127) are received (189), the scheduler (225) (or a transmitter (e.g., 245), or another device) linearly combines (191) the subset of the original packets according to the stored identifications, or the stored composition of the subsequent packet (e.g., 135), to generate the subsequent packet (e.g., 135).

A transmitter (e.g., 245) transmits (193), in the respective channel (e.g., 105), the subsequent packet (e.g., 135) after the transmission of the packets (e.g., 131, 133) that are scheduled for transmission in the respective channel (e.g., 105) before the subsequent packet (e.g., 135).

In one aspect, a method implemented in a computing apparatus includes: generating, by the computing apparatus, a plurality of first data packets (121, 123, 125, . . . , 127) of a same length from a data segment (111) to be transmitted via a plurality of parallel communication channels (105, 107, . . . , 109); and identifying, by the computing apparatus (e.g., using the scheduler (225)) from the first data packets (121, 123, 125, . . . , 127), a plurality of packet sequences (115, 117, . . . , 119) for the plurality of parallel communication channels (105, 107, . . . , 109) respectively. Each respective sequence (e.g., 115) of the plurality of packet sequences includes: one or a plurality of initial packets (e.g., 131) that are original packets (121, 123, 125, . . . , 127) and that are scheduled to be transmitted before subsequent packets (e.g., 133, 135, . . . , 139) in the respective sequence (e.g., 115); and subsequent packets (e.g., 135) that are linear combinations of a subset of the original packets (e.g., 121, 123, . . . , 127). The method further includes transmitting, by the computing apparatus (e.g., using the transmitters (245, 247, . . . , 249)), the plurality of sequences (115, 117, . . . , 119) of packets in the plurality of parallel communication channels (105, 107, . . . , 109) respectively.

During the transmitting, a recipient device (229) coupled to the plurality of parallel communication channels (105, 107, . . . , 109) is configured to determine whether a received set of packets (227), received via the parallel communication channels (105, 107, . . . , 109), is sufficient to reconstruct the data segment (111). In response to a determination that the received set of packets (227) is sufficient to reconstruct the data segment (111), the recipient device (229) directly terminates the transmitting of the sequences of channel-encoded packets. Alternatively, the recipient device (229) transmits an indicator to the computing apparatus to stop the transmitting of the sequences of channel-encoded packets.

In one embodiment of the aspect, the subsequent packet (135) is generated according to a forward error correction technique, where a randomly selected subset of the original packets (121, 123, 125, . . . , 127) are combined via a predetermined function (e.g., a linear combination, an exclusive or (XOR) operation).

In one embodiment of the aspect, the method includes distributing the plurality of original packets (e.g., 121, 123, 125, . . . , 127) to the plurality of packet sequences (e.g., 115, 117, . . . , 119) for the plurality of parallel communication channels (e.g., 105, 107, . . . , 109) respectively according to a round-robin schedule (163). Alternatively, the method includes distributing the plurality of original packets (e.g., 121, 123, 125, . . . , 127) to the plurality of packet sequences (e.g., 115, 117, . . . , 119) for the plurality of parallel communication channels (e.g., 105, 107, . . . , 109) sequentially.

In one embodiment of the aspect, the subsequent packet (e.g., 135) is selected to be linearly independent of packets (e.g., 131, 133) that include the original packet (e.g., 131) and that are scheduled to be transmitted in a respective channel (e.g., 105) before the subsequent packet (135). The subsequent packet may be further selected to be linearly independent of further packets (e.g., 141, . . . , 151) that are transmitted in the plurality of parallel communication channels (e.g., 107, . . . , 109) other than the respective channel (e.g., 105) in which the subsequent packet (135) is transmitted.

In another aspect, a method implemented in a computing apparatus includes: generating, by the computing apparatus, a plurality of original packets (121, 123, 125, . . . , 127) of a same length from a data segment (111) to be transmitted via a plurality of parallel communication channels (105, 107, . . . , 109); and identifying, by the computing apparatus (e.g., using the scheduler (225)) from the original packets, a plurality of packet sequences (115, 117, . . . , 119) for the plurality of parallel communication channels (105, 107, . . . , 109) respectively. Each respective sequence (e.g., 115) of the plurality of packet sequences includes a subsequent packet (e.g., 135) that is scheduled to be transmitted in a respective channel (e.g., 105) of the plurality of parallel communication channels and that is linearly independent of packets (e.g., 131, 133) that are scheduled to be transmitted in the respective channel (e.g., 105) before the subsequent packet (e.g., 135). Further, the subsequent packet (e.g., 135) is a linear combination of a subset of the original packets (e.g., 121, 123, 125, . . . , 127). The method further includes transmitting, by the computing apparatus (e.g., using the transmitters (245, 247, . . . , 249)), the plurality of sequences (115, 117, . . . , 119) of packets in the plurality of parallel communication channels (105, 107, . . . , 109) respectively. During the transmitting, a recipient device (229) coupled to the plurality of parallel communication channels (105, 107, . . . , 109) is configured to determine whether a received set of packets (227), received via the parallel communication channels (105, 107, . . . , 109), is sufficient to reconstruct the data segment (111); and in response to a determination that the received set of packets (227) is sufficient to reconstruct the data segment (111), the recipient device (229) directly terminates the transmitting of the sequences of channel-encoded packets. Alternatively, the recipient device (229) transmits an indicator to the computing apparatus to stop the transmission of the remaining parts of the sequences (115, 117, . . . , 119).

In one embodiment of this aspect, the subsequent packet (135) is further selected to be linearly independent of further packets (e.g., 141, . . . , 151) that are transmitted in the plurality of parallel communication channels (107, . . . , 109) other than the respective channel (105) in which the subsequent packet (135) is transmitted. For example, the further packets (e.g., 141, . . . , 151) are evenly distributed in the plurality of parallel communication channels (e.g., 107, . . . 109) other than the respective channel (105) in which the subsequent packet (135) is transmitted.

In one embodiment of this aspect, the further packets (141, . . . , 151) for the other channels (e.g., 107, . . . , 109) and the packets (e.g., 131, 133) that are scheduled to be transmitted in the respective channel (105) before the subsequent packet (135) form a base set (161) of packets; the base set (161) is selected to have fewer packets than the plurality of original packets (121, 123, 125, . . . , 127); and the subsequent packet (135) is selected to be linearly independent of the base set of data packets.

In one embodiment of this aspect, the subsequent packet (e.g., 135) is generated according to a forward error correction technique, which randomly selects the subset of the original packets (121, 123, 125, . . . , 127) according to a predetermined distribution, and combines the subset of the original packets (121, 123, 125, . . . , 127) using a linear function (e.g., exclusive or (XOR)). The random selection is repeated until the selected subset is linearly independent of the base set (161).

In one embodiment of this aspect, the method further includes: distributing the plurality of original packets (121, 123, 125, . . . , 127) to the plurality of packet sequences (115, 117, . . . , 119), according to a round-robin schedule (163), as initial packets of the packet sequences (115, 117, . . . , 119). Alternatively, the method further includes: distributing the plurality of original packets (121, 123, 125, . . . , 127) to the plurality of packet sequences (115, 117, . . . , 119) sequentially as initial packets of the packet sequences (115, 117, . . . , 119).

In a further aspect, a method implemented in a computing apparatus includes: identifying, by the computing apparatus (e.g., using the scheduler (225), compositions (e.g., 166) of a plurality of sequences (115, 117, . . . , 119) of packets to be transmitted respectively via a plurality of parallel communication channels (e.g., 105, 107, . . . , 109) to communicate a predetermined number of original packets (121, 123, 125, . . . , 127) of a same length to a recipient device (229). A composition (e.g., 166) of each respective packet (e.g., 143) in the plurality of sequences of packets includes an identification of each packet, among the original packets (121, 123, 125, . . . , 127), that is to be used to generate the respective packet (e.g., 143); and each respective sequence (e.g., 117) of the plurality of sequences includes at least one subsequent packet (143) that is a linear combination of a subset of the original packets (e.g., 121, 123, . . . , 125, 127) identified by a composition (e.g., 166) of the subsequent packet (143) to enable forward error correction. The computing apparatus stores the sequences (235, 237, . . . , 239) of compositions of the channel-encoded packets (e.g., 131, 133, 135, . . . , 139; 141, 143, 145, . . . , 149; 151, 153, 155, . . . , 159). After receiving a data segment (111), the computing apparatus generates the predetermined number of original packets (121, 123, 125, . . . , 127) from the data segment (111) and retrieves the sequences (235, 237, . . . , 239) of compositions to generate of the channel-encoded packets from the original packets (121, 123, 125, . . . , 127) according to the compositions. The computing apparatus uses the transmitters (235, 237, . . . 239) to transmit the plurality of sequences of channel-encoded packets (255, 257, . . . , 259) in the plurality of parallel communication channels (105, 107, . . . , 109) respectively. During the transmitting, the recipient device (229) determines whether a current set of received packets (227), received via the parallel communication channels (105, 107, 109), is sufficient to reconstruct the data segment (101); and if so, the recipient device (229) either directly terminates the transmission of remaining packets in each of the channels (105, 107, . . . , 109), or transmits an indicator to the computing apparatus (e.g., via the transmitters 245, 247, . . . , 249) to stop the transmission of remaining packets in each of the channels (105, 107, . . . , 109).

In one embodiment of this aspect, the identification of the sequences (115, 117, . . . , 119) includes initially distributing the plurality of original packets (121, 123, 125, . . . , 127) to the plurality of sequences (115, 117, . . . , 119) according to a round-robin or sequential schedule (163) as the initial packets of the sequences (115, 117, . . . , 119).

In one embodiment of this aspect, the channel-encoded packets are generated from the original packets (121, 123, 125, . . . , 127) according to the compositions based on an exclusive or (XOR) operation applied on subsets of the original packets (121, 123, 125, . . . , 127) identified by the compositions of the respective channel-encoded packets.

In one embodiment of this aspect, the composition (166) of the subsequent packet (143) is a randomly selected subset of the original packets (121, 123, 125, . . . , 127); and the randomly selected subset is selected such that it has a composition that is linearly independent of the compositions of: packets (123) that are queued in the respective sequence (117), in which the subsequent data packet (143) belongs, before the subsequent data packet (143); and one or more initial packets (121, 125, . . . ) that are queued in plurality of sequences (115, 119, . . . ) other than the respective sequence (117) in which the subsequent data packet (143) belongs.

The scheduler (225), the transmitters (245, 247, . . . , 249), the recipient device (229) and/or other devices used in the system of FIG. 6 and/or the methods discussed above can be implemented using a data processing system as illustrated in FIG. 13, with more or less components.

The performance of the communication systems discussed above (e.g., as illustrated in FIG. 1, 2, 3 or 6), or other communication systems that use forward error correction, can be optimized or improved for the transmission of a given data segment (111) by adjusting/optimizing the number of packets (121, 123, 125, . . . , 127) into which the data segment (111) is partitioned.

When the data segment (111) is partitioned into different numbers of packets (121, 123, 125, . . . , 127) for transmission using a forward error correction technique, the transmission has different data communication overheads and/or computation overheads. The cost of the overheads can be evaluated as a function of the number of packets used in partitioning the data segment (111) of a given size. An optimized number of packets used in partitioning the data segment (111) is then determined from the cost function.

FIG. 9 illustrates an overhead cost in data communication for transmitting a data segment by dividing the data segment into a plurality of data packets for forward error control.

In FIG. 9, the data segment (111) has a data size of L (e.g., measured in bytes when the smallest unit of data communication in the system is a byte). When the data segment (111) is partitioned into K packets of an equal size P, it is typical that the sum of sizes (e.g., K*P) of the packets (121, 123, 125, . . . , 127) does not equal to the size L of the data segment (111); and as a result, some or all of the packets (121, 123, 125, . . . , 127) have dummy data (e.g., with zeros, ones, or random data) added therein to ensure that the packets (121, 123, 125, . . . , 127) have the same size P. The sum of the overheads (231, 233, 235, . . . , 237) in the data packets (121, 123, 125, . . . , 127) due to the padding provides the size of the data overhead (241) (e.g., K*P−L).

When the data (221, 223, 225, . . . , 227) of the data segment (111) is distributed to K data packets (121, 123, 125, . . . , 127), the minimum size P for the data packets (121, 123, 125, . . . , 127) is the smallest integer that is greater than or equal to L/K.

The data (221, 223, 225, . . . , 227) of an equally length can be distributed from the data segment (111) to the packets (121, 123, 125, . . . , 127) such that the overheads (231, 233, 235, . . . , 237) in the packets (e.g., in the form of padded zeros, ones or random data) have an equal length.

Alternatively, different packets (e.g., 121, 123, 125, . . . , 127) may have overheads (231, 233, 235, . . . , 237) of different sizes. For example, each of the packets (121, 123, 125, . . . ) except the last packet (127) has no overhead in one arrangement; and the last packet (127) carries the entire data overhead (241) (e.g., K*P−L, where P is at least the smallest integer that is greater than or equal to L/K).

Transmitting the data overhead (241) is the extra cost for transmitting the data segment (111) by dividing the data segment (111) into the packets (121, 123, 125, . . . , 127) of the same length for channel encoding using a forward error correction technique.

The original packets (121, 123, 125, . . . , 127) having the data overhead (241) can be used to generate the packets in the copies (115, 117, . . . , 119) for transmission over parallel channels (105, 107, . . . , 109), as illustrated in FIGS. 1-8.

FIG. 10 illustrates the data structure of a communication packet of one embodiment.

For example, the communication packet (243) can be used to transmit a typical packet in the copies (115, 117, . . . , 119) illustrated in FIG. 1, 2, or 3, or one of the channel-encoded packets (225, 257, . . . , 259) illustrated in FIG. 6.

In FIG. 10, the communication packet (243) includes a plurality of data fields to provide information that can be used for decoding. For example, the communication packets (243) includes fields specifying the number of packets K (251), the number of padded zeros (or ones, or random data, or dummy data) (253) in the coded data payload (257), and the coefficient vector (255) (e.g., the composition (166) of a channel-encoded packet (143)) used to generate the coded data payload (257) from the packets (121, 123, 125, . . . , 127), in addition to the field for the coded data payload (257) that has the size P.

The coefficient vector (255) identifies the composition vector (e.g., 166) of a channel-encoded packet (243). The first K bits of the coefficient vector (255), as identified by the field of number of packets K (251), correspond to the K original packets (121, 123, 125, . . . , 127) respectively. When the i'th bit in the coefficient vector (255) has a first value (e.g., 1), the i'th packet in the packets (121, 123, 125, . . . , 127) is used to generate the coded data payload (257) transmitted via the communication packet (243); and when the i'th bit in the coefficient vector (255) has a second value (e.g., 0), the i'th packet in the packets (121, 123, 125, . . . , 127) is not used to generate the coded data payload (257) transmitted via the communication packet (243). The data fields (251, 253, and 255) for providing the information to assist the recipient device (229) in decoding the coded data payloads (e.g., 257) are the overhead (245) in the communication packet (243).

The number of packets K (251) and the number of padded zeros (ones, random data, or dummy data) (253) in the coded data payload (257) can be transmitted for each communication packet used to transmit a packet in the copies (e.g., 115, 117, . . . , 119). In other implementations, the number of packets K (251) and the number of padded zeros (or ones or random data) (253) in the coded data payload (257) are transmitted only once for each of the copies (e.g., 115, 117, . . . , 119) to reduce overhead. In other implementations, additional data fields may be included for each communication packet (243).

The number of packets K (251) is typically limited to be less than a predetermined limit (e.g., 256). Thus, the size of data field for the number of packets K (251) is predetermined (e.g., 1 byte) does not change as a function of the number of packets K (251). Further, the data field for the number of padded zeros (or ones or random data) (253) has a predetermined size (e.g., 4 bytes) that is not a function of the number of packets K (251).

However, the size of the field of the coefficient vector (255) typically changes as a function of the number of packets K (251). For example, the minimum size Q of the coefficient vector (255) (e.g., in bytes) is equal to the smallest integer that is greater than or equal to K/8.

FIG. 11 illustrates various cost considerations in the transmission of a data segment using a forward error correction technique.

In FIG. 11, partitioning (101) the data segment (111) having a size L into the original packets (121, 123, 125, . . . , 127) having an equal size P results in the data overhead (241) as illustrated in FIG. 9. The cost of transmitting the padded zeros (ones, random data, or dummy data) corresponding to the transmission cost of the data overhead (241).

In FIG. 11, transmitting each packet (e.g., 131, 133, 135, . . . , 139; 141, 143, 145, . . . , 149; . . . ; 151, 153, 157, . . . , or 159) using the forward error correction technique results in the transmission of additional data fields (e.g., 251, 253, 255 illustrated in FIG. 10) and thus the overhead (245). The cost of transmitting the overhead in each communication packet (243) used to carry a respective data packet in the copies (115, 117, . . . , 119) corresponds to the cost of transmitting communication packet overhead.

In FIG. 11, there is a computation cost of the forward error correction technique in encoding (103) the original packets into the packets (115, 117, . . . , 119) and/or decoding the copies to generate the recovered data segment (113). The computation cost is typically a function of the number of original packets K (251) into which the data segment (111) is partitioned. When fountain codes are used in FEC, the cost of the computational complexity is typically in the order of log (K). Alternatively, the cost function of computational complexity may be empirically measured, or derived from curving a set of data points.

Further, due to the uncertainty in the communication system (e.g., random delay in the channels), the actual number of packets the recipient device (229) will receive from each of the channels (105, 107, . . . , 109) is random before the recipient device (229) obtains sufficient packets for decoding (104) and then prevents the further transmission of the remaining packets. This introduces uncertainty in usefulness of the received packets, which causes that more than K communication packets are communicated via the channels (105, 107, . . . , 109) as a whole before the recipient device (229) receives a sufficient number (e.g., K) of useful packets for the generation of the recovered data segment (113) and thus terminates the transmission. The exact number of additional communication packets transmitted via the system changes as the uncertainty in the communication system (e.g., random delays in the channels in transmitting the packets of the copies). An estimated (or average number, or an upper limit) of the additional communication packets over the number of packets K can be used to determine the cost of transmitting redundant packets (not useful packet for decoding the channel-encoded packets).

For example, when the copies (115, 117, 119) are generated using a round-robin (or sequential) allocation (163) scheme (e.g., as illustrated in FIG. 4) with subsequent channel-encoded packets generated to be linearly independent of their base sets (e.g., as illustrated in FIG. 5), no more than K+d communication packets (e.g., d=3) are expected to be transmitted in the communication system over the parallel communication channels (1105, 107, . . . , 109), before the transmission can be terminated. Thus, the cost of transmitting the redundant packets can be estimated as the size of the additional d communication packets.

For example, when the data segment of a size L is partitioned (101) into K original packets (121, 123, 125, . . . , 127), the minimal size P of each original packets (121, 123, 125, . . . , 127) is the smallest integer that is large than or equal to L/K. Thus, the field for coded data payload (257) of the communication packet has a size of P. The field for the coefficient vector (255) has a size of Q which is at least the smallest integer that is larger than or equal to K/8. When the communication packet uses one byte to transmit the number of packets (251), four bytes to transmit the number of padded zeros (253) (or padded ones, random data or dummy data), the size of the communication packet (243) is (5+Q+P). When K+d (e.g., d=3) of communication packets (243) are used to transmit the data segment in order for the recipient device (229) to generate the recovered data segment (113), the total size of the transmitted communication packets is (5+Q+P)*(K+d); and the bandwidth cost, including the cost for transmitting the data overhead (241), the cost for transmitting the communication packet overhead (245), and cost for transmitting the redundant packets transmitted before the termination, is proportional to (5+Q+P)*(K+d). The cost of FEC encoding (103) and/or decoding (104) is typically proportional to L*log (K).

The cost of FEC encoding (103) and/or decoding (104) and the cost of the communication (e.g., data overhead (241), communication packet overhead (245), redundant packets) may have different weight. Different weights can be assigned to the computation cost and the communication cost to generate a combined cost function of the number K to partition (101) the data segment (111) into the original K packets (121, 123, 125, . . . , 127). An optimized K can be determined from the cost function for the partition (101) of the data segment (111).

FIG. 12 shows a method to transmit a data segment according to one embodiment.

In FIG. 12, after receiving (261) the size L of a data segment (111) to be divided into original packets (121, 123, 125, . . . , 127) for transmission using a forward error correction (FEC) coding technique, a computing device is configured to compute (263) a cost of transmitting the data segment (111) using the FEC coding technique by dividing the data segment (111) into a predetermined number K of original packets (121, 123, 125, . . . , 127). The cost may include the communication cost of the data overhead (241) as illustrated in FIG. 9, the communication cost of the overhead (245) in communication packet (243) as illustrated in FIG. 10, the computing cost of the FEC coding technology as illustrated in and discussed in connection with FIG. 11, and/or the communication cost of the redundant packets, as illustrated in and discussed in connection with FIG. 11.

In FIG. 12, the computing device adjusts (265) the number K to identify a number K′ to minimize the cost of transmitting the data segment.

After the number K′ is identified, the computing device divides (267) the data segment (111) of size L into the number K′ of original packets (121, 123, 125, . . . , 127), generates (269) channel-encoded packets (e.g., 131, 133, 135, . . . , 139; 141, 143, 145, . . . 149; . . . ; 151, 153, . . . , 159) from the number K′ of original packets (121, 123, 125, . . . , 127), and transmit (271) the channel-encoded packets (e.g., 131, 133, 135, . . . , 139; 141, 143, 145, . . . 149; . . . ; 151, 153, . . . , 159) using a plurality of parallel communication channels (105, 107, . . . , 109).

For example, the method of FIG. 12 can be implemented in a system illustrated in FIG. 11. The copies (115, 117, . . . , 119) of packets to be transmitted via the parallel communication channels (105, 107, . . . , 109) can be generated using the techniques of FIG. 2 or 3, where the distribution of systematic packets can be performed using the technique of FIG. 4, and the compositions of subsequent channel-encoded packets can be identified using the technique of FIG. 5. Further, the compositions can be pre-computed in a way as illustrated in FIG. 6.

In some implementations, an explicit expression is derived for the cost as a function of the number K of original packets into which the data segment (111) of the size L is partitioned (101). An explicit function can be derived to compute the optimized K′ as a function of the size L of the data segment (111) to be transmitted.

In some implementations, a table of optimized K′ is pre-computed as a function of the size L of the data segment (111) for a particular communication system (e.g., having its unique weight of the communication cost for communication over the channels (105, 107, . . . , 109) and the computation cost for FEC encoding (103) and/or decoding (104). Subsequently, the optimized K′ for a given size L of a particular data segment (111) can be looked up from the table.

In some implementations, an empirical formula (e.g., generated from curve fitting the table of K′ vs. L) is used to compute the optimized number K′ of division from a given size L of the data segment (111).

In some implementations, the optimized K′ is computed just in time for the transmission of the data segment (111) having the size L, in view of the cost characteristics of the communication system available to transmit the data segment (111) using a FEC technique.

In one aspect, a method implemented in a computing apparatus includes: receiving, in the computing apparatus, a size L of a data segment (111) to be transmitted by the computing apparatus; and determining, by the computing apparatus, a number K by optimizing a cost of transmitting the data segment (111), such that the data segment (111) is divided into the number K of original packets (121, 123, 125, . . . , 127) based on which channel-encoded packets (e.g., 143 in FIG. 2 or 5), are generated for transmission using a forward error correction technique. Any optimization techniques can be used to search for and/or compute the optimal K from the function of the cost of transmitting the data segment (111).

In one embodiment of the aspect, after the optimal K is determined, the computing apparatus partitions (101) the data segment (101) having the size L into the number K of original packets (121, 123, 125, . . . , 127), generates a plurality of copies (115, 117, . . . , 119) of packets from the original packets (121, 123, 125, . . . , 127) using the forward error correction technique, and transmits, to a recipient device (229), the plurality of copies (115, 117, . . . , 119) of packets using a plurality of parallel communication channels (105, 107, . . . , 109) respectively. The recipient device (229) determines whether a received set of packets received via the parallel communication channels (105, 107, . . . , 109) is sufficient to generate the recovered data segment (113), and if so, causes termination of the transmission of the copies (115, 117, . . . , 119), when sufficient numbers of useful packets have been received in the recipient device from the channels (105, 107, . . . , 109).

The cost of transmission considered for the optimization may include: first data transmission cost for dummy data (e.g., overhead 241) added to the original packets (121, 123, 125, . . . , 127) so that the original packets have a same size P; second data transmission cost for data in communication fields (e.g., 251, 253, 255) added in communication packets (e.g., 243) to enable decoding using the forward error correction technique (e.g., overhead 245); and/or third data transmission cost for redundant communication packets that are expect to be transmitted to the recipient device (229) before the termination of the transmission. The third data transmission cost can be estimated based on a count of maximum (or average, or expected) redundant communication packets that are expected to be transmitted via the parallel channels (105, 107, . . . , 109) before the termination of the transmission of the copies (115, 117, . . . , 119). When the techniques for generating the copies (115, 117, . . . , 119) as illustrated in FIGS. 1-5 are used, the count is typically three using communication channels that each can transmit data reliably but may have different and/or varying transmission speeds.

Further, the cost of transmission considered for the optimization may include computation cost associated with application of the forward error correction technique, which is typically proportional to a logarithm function of the number K of original packets (121, 123, 125, . . . , 127).

Typically, the number K of original packets is limited to be no more than 256. The cost for different values of K can be computed individually to find the optimal K that minimizes the cost of transmission.

When the technique of FIG. 4 is used, the plurality of copies (115, 117, . . . , 119) can be generated from the original packets (121, 123, . . . , 125, 127) by distributing the original packets (121, 123, . . . , 125, 127) to the copies according to a round-robin scheme or a sequential scheme as the initial/leading packets of the copies (115, 117, . . . , 119).

When the technique of FIG. 5 is used, the plurality of copies (115, 117, . . . , 119) can be generated from the original packets (121, 123, . . . , 125, 127) by selecting a subset of the original packets (e.g., as identified by the composition (166) in FIG. 5) such that the subset is linearly independent on a base set (165) of packets in the copies (115, 117, . . . , 119). A subsequent channel-encoded packet (e.g., 143) is generated from the subset for transmitting in a particular copy (117) of the plurality of copies (e.g., 115, 117, . . . , 119). The base set includes one or more packets (e.g., 123) of the particular copy that are scheduled to be transmitted before the subsequent channel-encoded packet (143). The base set may further include at least initial packet (e.g., packet (121) in copy (115), packet (125) in copy (119)) in each of the plurality of copies. Preferably, the subset does not include any of original packets (e.g., 123) allocated to the particular copy (117).

For example, the subsequent channel-encoded packet (143) can be generated from exclusive or of the packets in the subset; and the subset is selected randomly according to a predetermined distribution. The random selection can be repeated until the selected subset is linearly independent of the base set (165) and/or does not include any of the original packets allocated to the particular copy (117) and/or does not include any of the original packets in the base set (165).

The present disclosure includes the methods discussed above, computing apparatuses configured to perform methods, and computer storage media storing instructions which when executed on the computing apparatuses causes the computing apparatuses to perform the methods.

FIG. 13 shows a data processing system on which the methods of the present disclosure can be implemented. While FIG. 13 illustrates various components of a computer system, it is not intended to represent any particular architecture or manner of interconnecting the components. One embodiment may use other systems that have fewer or more components than those shown in FIG. 13.

In FIG. 13, the data processing system (200) includes an inter-connect (201) (e.g., bus and system core logic), which interconnects a microprocessor(s) (203) and memory (211). The microprocessor (203) is coupled to cache memory (209) in the example of FIG. 13.

In one embodiment, the inter-connect (201) interconnects the microprocessor(s) (203) and the memory (211) together and also interconnects them to input/output (I/O) device(s) (205) via I/O controller(s) (207). I/O devices (205) may include a display device and/or peripheral devices, such as mice, keyboards, modems, network interfaces, printers, scanners, video cameras and other devices known in the art. In one embodiment, when the data processing system is a server system, some of the I/O devices (205), such as printers, scanners, mice, and/or keyboards, are optional.

In one embodiment, the inter-connect (201) includes one or more buses connected to one another through various bridges, controllers and/or adapters. In one embodiment the I/O controllers (207) include a USB (Universal Serial Bus) adapter for controlling USB peripherals, and/or an IEEE-1394 bus adapter for controlling IEEE-1394 peripherals.

In one embodiment, the memory (211) includes one or more of: ROM (Read Only Memory), volatile RAM (Random Access Memory), and non-volatile memory, such as hard drive, flash memory, etc.

Volatile RAM is typically implemented as dynamic RAM (DRAM) which requires power continually in order to refresh or maintain the data in the memory. Non-volatile memory is typically a magnetic hard drive, a magnetic optical drive, an optical drive (e.g., a DVD RAM), or other type of memory system which maintains data even after power is removed from the system. The non-volatile memory may also be a random access memory.

The non-volatile memory can be a local device coupled directly to the rest of the components in the data processing system. A non-volatile memory that is remote from the system, such as a network storage device coupled to the data processing system through a network interface such as a modem or Ethernet interface, can also be used.

In this description, some functions and operations are described as being performed by or caused by software code to simplify description. However, such expressions are also used to specify that the functions result from execution of the code/instructions by a processor, such as a microprocessor.

Alternatively, or in combination, the functions and operations as described here can be implemented using special purpose circuitry, with or without software instructions, such as using Application-Specific Integrated Circuit (ASIC) or Field-Programmable Gate Array (FPGA). Embodiments can be implemented using hardwired circuitry without software instructions, or in combination with software instructions. Thus, the techniques are limited neither to any specific combination of hardware circuitry and software, nor to any particular source for the instructions executed by the data processing system.

While one embodiment can be implemented in fully functioning computers and computer systems, various embodiments are capable of being distributed as a computing product in a variety of forms and are capable of being applied regardless of the particular type of machine or computer-readable media used to actually effect the distribution.

At least some aspects disclosed can be embodied, at least in part, in software. That is, the techniques may be carried out in a computer system or other data processing system in response to its processor, such as a microprocessor, executing sequences of instructions contained in a memory, such as ROM, volatile RAM, non-volatile memory, cache or a remote storage device.

Routines executed to implement the embodiments may be implemented as part of an operating system or a specific application, component, program, object, module or sequence of instructions referred to as “computer programs.” The computer programs typically include one or more instructions set at various times in various memory and storage devices in a computer, and that, when read and executed by one or more processors in a computer, cause the computer to perform operations necessary to execute elements involving the various aspects.

A machine readable medium can be used to store software and data which when executed by a data processing system causes the system to perform various methods. The executable software and data may be stored in various places including for example ROM, volatile RAM, non-volatile memory and/or cache. Portions of this software and/or data may be stored in any one of these storage devices. Further, the data and instructions can be obtained from centralized servers or peer to peer networks. Different portions of the data and instructions can be obtained from different centralized servers and/or peer to peer networks at different times and in different communication sessions or in a same communication session. The data and instructions can be obtained in entirety prior to the execution of the applications. Alternatively, portions of the data and instructions can be obtained dynamically, just in time, when needed for execution. Thus, it is not required that the data and instructions be on a machine readable medium in entirety at a particular instance of time.

Examples of computer-readable media include but are not limited to recordable and non-recordable type media such as volatile and non-volatile memory devices, read only memory (ROM), random access memory (RAM), flash memory devices, floppy and other removable disks, magnetic disk storage media, optical storage media (e.g., Compact Disk Read-Only Memory (CD ROM), Digital Versatile Disks (DVDs), etc.), among others. The computer-readable media may store the instructions.

The instructions may also be embodied in digital and analog communication links for electrical, optical, acoustical or other forms of propagated signals, such as carrier waves, infrared signals, digital signals, etc. However, propagated signals, such as carrier waves, infrared signals, digital signals, etc. are not tangible machine readable medium and are not configured to store instructions.

In general, a machine readable medium includes any mechanism that provides (i.e., stores and/or transmits) information in a form accessible by a machine (e.g., a computer, network device, personal digital assistant, manufacturing tool, any device with a set of one or more processors, etc.).

In various embodiments, hardwired circuitry may be used in combination with software instructions to implement the techniques. Thus, the techniques are neither limited to any specific combination of hardware circuitry and software nor to any particular source for the instructions executed by the data processing system.

Other Aspects

The description and drawings are illustrative and are not to be construed as limiting. The present disclosure is illustrative of inventive features to enable a person skilled in the art to make and use the techniques. Various features, as described herein, should be used in compliance with all current and future rules, laws and regulations related to privacy, security, permission, consent, authorization, and others. Numerous specific details are described to provide a thorough understanding. However, in certain instances, well known or conventional details are not described in order to avoid obscuring the description. References to one or an embodiment in the present disclosure are not necessarily references to the same embodiment; and, such references mean at least one.

The use of headings herein is merely provided for ease of reference, and shall not be interpreted in any way to limit this disclosure or the following claims.

Reference to “one embodiment” or “an embodiment” means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the disclosure. The appearances of the phrase “in one embodiment” in various places in the specification are not necessarily all referring to the same embodiment, and are not necessarily all referring to separate or alternative embodiments mutually exclusive of other embodiments. Moreover, various features are described which may be exhibited by one embodiment and not by others. Similarly, various requirements are described which may be requirements for one embodiment but not other embodiments. Unless excluded by explicit description and/or apparent incompatibility, any combination of various features described in this description is also included here. For example, the features described above in connection with “in one embodiment” or “in some embodiments” can be all optionally included in one implementation, except where the dependency of certain features on other features, as apparent from the description, may limit the options of excluding selected features from the implementation, and incompatibility of certain features with other features, as apparent from the description, may limit the options of including selected features together in the implementation.

The disclosures of the above discussed patent documents are hereby incorporated herein by reference.

In the foregoing specification, the disclosure has been described with reference to specific exemplary embodiments thereof. It will be evident that various modifications may be made thereto without departing from the broader spirit and scope as set forth in the following claims. The specification and drawings are, accordingly, to be regarded in an illustrative sense rather than a restrictive sense. 

What is claimed is:
 1. A method implemented in a computing apparatus, the method comprising: dividing, by the computing apparatus, a data segment to be transmitted by the computing apparatus into a number of original packets; generating, by the computing apparatus, a plurality of copies of packets from the original packets by applying a forward error correction technique for each of the plurality of copies of packets; and transmitting, by the computing apparatus to a recipient device, the plurality of copies of packets using a plurality of parallel communication channels, such that a respective copy of the plurality of copies is transmitted over a corresponding communication channel of the plurality of parallel communication channels, wherein the recipient device determines whether a received set of packets received via the parallel communication channels is sufficient to reconstruct the data segment, and causes termination of the transmitting in response to a determination that the received set of packets is sufficient to reconstruct the data segment.
 2. The method of claim 1, wherein the dividing is based on a cost of transmission, which includes a first data transmission cost for dummy data added to the original packets so that the original packets have a same size.
 3. The method of claim 2, wherein the cost of transmission includes a second data transmission cost for data in communication fields added in communication packets to enable decoding using the forward error correction technique.
 4. The method of claim 3, wherein the cost of transmission includes a third data transmission cost for redundant communication packets that are expect to be transmitted to the recipient device before the termination of the transmitting.
 5. The method of claim 4, wherein the cost of transmission includes a computation cost associated with the applying the forward error correction technique.
 6. The method of claim 5, wherein the number of original packets is less than or equal to
 256. 7. The method of claim 5, wherein a count of the redundant communication packets used in computing the cost is three.
 8. The method of claim 5, wherein the computation cost associated with application of the forward error correction technique is proportional to a logarithm function of the number of original packets.
 9. The method of claim 5, wherein the generating of the plurality of copies of packets from the original packets includes distributing the original packets to the copies according to a round-robin scheme or a sequential scheme.
 10. The method of claim 9, wherein the generating of the plurality of copies of packets from the original packets includes: selecting a subset of the original packets, wherein the subset is linearly independent of a base set of packets in the copies; and generating a channel-encoded packet from the subset for transmitting in a first copy of the plurality of copies.
 11. The method of claim 10, wherein the base set includes one or more packets of the first copy that are scheduled to be transmitted before the channel-encoded packet.
 12. The method of claim 11, wherein the base set includes at least an initial packet in each of the plurality of copies.
 13. The method of claim 11, wherein the subset does not include any of original packets allocated to the first copy.
 14. The method of claim 11, wherein the channel-encoded packet is generated from exclusive or of the subset.
 15. The method of claim 11, wherein the subset is selected randomly according to a predetermined distribution.
 16. A non-transitory computer storage medium storing instructions which, when executed by a computing apparatus, cause the computing apparatus to perform a method, the method comprising: dividing, by the computing apparatus, a data segment to be transmitted by the computing apparatus into a number of original packets; generating, by the computing apparatus, a plurality of copies of packets from the original packets by applying a forward error correction technique for each of the plurality of copies of packets; and transmitting, by the computing apparatus to a recipient device, the plurality of copies of packets using a plurality of parallel communication channels, such that a respective copy of the plurality of copies is transmitted over a corresponding communication channel of the plurality of parallel communication channels, wherein the recipient device determines whether a received set of packets received via the parallel communication channels is sufficient to reconstruct the data segment, and causes termination of the transmitting in response to a determination that the received set of packets is sufficient to reconstruct the data segment.
 17. A computing apparatus, comprising: at least one microprocessor; and memory storing instructions configured to instruct the at least one microprocessor to: partition, by the computing apparatus, data segment to be transmitted by the computing apparatus into a number of original packets; generate, by the computing apparatus, a plurality of copies of packets from the original packets by applying a forward error correction technique for each of the plurality of copies of packets; and transmit, by the computing apparatus to a recipient device, the plurality of copies of packets using a plurality of parallel communication channels, such that a respective copy of the plurality of copies is transmitted over a corresponding communication channel of the plurality of parallel communication channels, wherein the recipient device determines whether a received set of packets received via the parallel communication channels is sufficient to reconstruct the data segment, and in response to a determination that the received set of packets is sufficient to reconstruct the data segment, causes termination of transmission of the copies.
 18. The computing apparatus of claim 17, wherein the instructions are configured to instruct the at least one processor to partition the data segment based on a cost of transmission, which includes: a first data transmission cost for dummy data added to the original packets so that the original packets have a same size; a second data transmission cost for data in communication fields added in communication packets to enable decoding using the forward error correction technique; and a third data transmission cost for redundant communication packets that are expected to be transmitted to the recipient device before the termination of the transmitting.
 19. The computing apparatus of claim 18, wherein the cost of transmission further includes a cost of computational complexity associated with the applying of the forward error correction technique.
 20. The computing apparatus of claim 19, wherein the third data transmission cost is based on a maximum count of the redundant communication packets. 